Error correction on quantum devices

Abstract

A method of quantum error correction may include obtaining a logical qubit including a logical state. The logical qubit may be encoded using a quantum code to determine states for a plurality of physical qubits, the quantum code including a first code generated based on a first set of generators and a second code generated based on a second set of generators, the first set of generators and the second set of generators including different cardinality. The method may further include adjusting physical states of the plurality of physical qubits in quantum hardware based on the determined states. One or more computations may be performed using the quantum hardware and the physical states of the plurality of physical qubits may be decoded using the quantum code to determine the logical state.

What is claimed is: 
     
         1 . A method, comprising:
 obtaining a logical qubit including a logical state;   encoding the logical qubit using a quantum code to determine states for a plurality of physical qubits, the quantum code including a first code generated based on a first set of generators and a second code generated based on a second set of generators, the first set of generators and the second set of generators including different cardinality;   adjusting physical states of the plurality of physical qubits in quantum hardware based on the determined states;   performing one or more computations using the quantum hardware; and   decoding the physical states of the plurality of physical qubits using the quantum code to determine the logical state.   
     
     
         2 . The method of  claim 1 , wherein a quantum code rate of the quantum code is selected from a particular subset of potential code rates, the particular subset selected such that the quantum code rate is greater than a code rate where a first code rate equals one minus a second code rate, where the first code rate is of the first code and the second code rate is of the second code. 
     
     
         3 . The method of  claim 2 , wherein the first code rate is determined using a dimensionality of the first set of generators and the second code rate is determined using a dimensionality of the second set of generators. 
     
     
         4 . The method of  claim 2 , wherein the first code rate is between 0.5 and 1, and the second code rate is between 0 and 0.5. 
     
     
         5 . The method of  claim 2 , wherein the first code rate is between 0 and 0.5, and the second code rate is between 0.5 and 1. 
     
     
         6 . The method of  claim 1 , wherein the first set of generators and the second set of generators are symmetric subsets of a group. 
     
     
         7 . The method of  claim 6 , wherein the group is an infinite group. 
     
     
         8 . The method of  claim 1 , wherein the first code includes bit-flip generators and the second code includes phase-flip generators. 
     
     
         9 . The method of  claim 1 , wherein the encoding the logical qubit with the plurality of physical qubits include mapping the logical qubit logical state of the logical qubit to the plurality of physical qubits. 
     
     
         10 . One or more non-transitory computer-readable media storing instructions that, when executed by one or more processors, cause a system to perform operations, the operations comprising:
 obtaining a logical qubit including a logical state;   encoding the logical qubit using a quantum code to determine states for a plurality of physical qubits, the quantum code including a first code generated based on a first set of generators and a second code generated based on a second set of generators, the first set of generators and the second set of generators including different cardinality;   adjusting physical states of the plurality of physical qubits in quantum hardware based on the determined states;   performing one or more computations using the quantum hardware; and   decoding the physical states of the plurality of physical qubits using the quantum code to determine the logical state.   
     
     
         11 . The one or more non-transitory computer-readable media of  claim 10 , wherein a quantum code rate of the quantum code is selected from a particular subset of potential code rates, the particular subset selected such that the quantum code rate is greater than a code rate where a first code rate equals one minus a second code rate, where the first code rate is of the first code and the second code rate is of the second code. 
     
     
         12 . The one or more non-transitory computer-readable media of  claim 11 , wherein the first code rate is determined using a dimensionality of the first set of generators and the second code rate is determined using a dimensionality of the second set of generators. 
     
     
         13 . The one or more non-transitory computer-readable media of  claim 11 , wherein the first code rate is between 0.5 and 1, and the second code rate is between 0 and 0.5. 
     
     
         14 . The one or more non-transitory computer-readable media of  claim 11 , wherein the first code rate is between 0 and 0.5, and the second code rate is between 0.5 and 1. 
     
     
         15 . The one or more non-transitory computer-readable media of  claim 10 , wherein the first set of generators and the second set of generators are symmetric subsets of a group. 
     
     
         16 . The one or more non-transitory computer-readable media of  claim 15 , wherein the group is an infinite group. 
     
     
         17 . The one or more non-transitory computer-readable media of  claim 10 , wherein the first code includes bit-flip generators, and the second code includes phase-flip generators. 
     
     
         18 . The one or more non-transitory computer-readable media of  claim 10 , wherein the encoding the logical qubit with the plurality of physical qubits include mapping the logical qubit logical state of the logical qubit to the plurality of physical qubits. 
     
     
         19 . A system, comprising:
 one or more processors; and   one or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause the system to perform operations, the operations comprising:   obtaining a logical qubit including a logical state;   encoding the logical qubit using a quantum code to determine states for a plurality of physical qubits, the quantum code including a first code generated based on a first set of generators and a second code generated based on a second set of generators, the first set of generators and the second set of generators including different cardinality;   adjusting physical states of the plurality of physical qubits in quantum hardware based on the determined states;   performing one or more computations using the quantum hardware; and   decoding the physical states of the plurality of physical qubits using the quantum code to determine the logical state.   
     
     
         20 . The system of  claim 19 , wherein a quantum code rate of the quantum code is selected from a particular subset of potential code rates, the particular subset selected such that the quantum code rate is greater than a code rate where a first code rate equals one minus a second code rate, where the first code rate is of the first code and the second code rate is of the second code.